Evolutionary modelling and analysis of voluntary participation has been considered in several studies [1]}, [2]}, [3]}, [4]}, [5]}.
However, these works did not consider strategies conditioned on the formation of a commitment (nor incentives for encouraging the participation in it). Typically only a subset of unconditional strategies were considered, including cooperators, defectors and non-participants. Here we have examined a full set of strategies (Table REF ). In contrast to these studies, we have shown that the evolutionary stable strategies often exhibit behaviours conditional on the formation of commitment being formed; e.g., see ESS strategies ACD and NDC in Figure REF . Given this crucial limitation of previous works, our model here provides a more complete picture of how prior commitments such as formal and informal contracts and agreements, provides an efficient mechanism for promoting the evolution of cooperation.
